The lifespans of porcupines in a particular zoo are normally distributed. The average porcupine lives $22.2$ years; the standard deviation is $3.3$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a porcupine living between $25.5$ and $28.8$ years.
Explanation: $22.2$ $18.9$ $25.5$ $15.6$ $28.8$ $12.3$ $32.1$ $95\%$ $68\%$ $13.5\%$ $13.5\%$ We know the lifespans are normally distributed with an average lifespan of $22.2$ years. We know the standard deviation is $3.3$ years, so one standard deviation below the mean is $18.9$ years and one standard deviation above the mean is $25.5$ years. Two standard deviations below the mean is $15.6$ years and two standard deviations above the mean is $28.8$ years. Three standard deviations below the mean is $12.3$ years and three standard deviations above the mean is $32.1$ years. We are interested in the probability of a porcupine living between $25.5$ and $28.8$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the porcupines will have lifespans within 2 standard deviations of the average lifespan. It also tells us that $68\%$ of the porcupines will have lifespans within 1 standard deviation of the mean. The probability of a particular porcupine living between $25.5$ and $28.8$ years is $\color{orange}{13.5\%}$.